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Langlands Group
In mathematics, the Langlands group is a conjectural group ''L''''F'' attached to each local or global field ''F'', that satisfies properties similar to those of the Weil group. It was given that name by Robert Kottwitz. In Kottwitz's formulation, the Langlands group should be an extension of the Weil group by a compact group. When ''F'' is local archimedean, ''LF'' is the Weil group of ''F'', when ''F'' is local non-archimedean, ''LF'' is the product of the Weil group of ''F'' with SU(2). When ''F'' is global, the existence of ''LF'' is still conjectural, though James Arthur gives a conjectural description of it. The Langlands correspondence for ''F'' is a "natural" correspondence between the irreducible ''n''-dimensional complex representations of ''LF'' and, in the local case, the cuspidal automorphic representations of GL''n''(A''F''), where A''F'' denotes the adele Adele Laurie Blue Adkins (, ; born 5 May 1988), professionally kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a Set (mathematics), set and an Binary operation, operation that combines any two Element (mathematics), elements of the set to produce a third element of the set, in such a way that the operation is Associative property, associative, an identity element exists and every element has an Inverse element, inverse. These three axioms hold for Number#Main classification, number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weil Group
In mathematics, a Weil group, introduced by , is a modification of the absolute Galois group of a local or global field, used in class field theory. For such a field ''F'', its Weil group is generally denoted ''WF''. There also exists "finite level" modifications of the Galois groups: if ''E''/''F'' is a finite extension, then the relative Weil group of ''E''/''F'' is ''W''''E''/''F'' = ''WF''/ (where the superscript ''c'' denotes the commutator subgroup). For more details about Weil groups see or or . Weil group of a class formation The Weil group of a class formation with fundamental classes ''u''''E''/''F'' ∈ ''H''2(''E''/''F'', ''A''''F'') is a kind of modified Galois group, used in various formulations of class field theory, and in particular in the Langlands program. If ''E''/''F'' is a normal layer, then the (relative) Weil group ''W''''E''/''F'' of ''E''/''F'' is the extension :1 → ''A''''F'' → ''W''''E''/''F'' → Gal(''E''/''F'') → 1 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Kottwitz
Robert Edward Kottwitz (born 1950 in Lynn, Massachusetts) is an American mathematician. Kottwitz studied at the University of Washington (B.A.) and then went to Harvard University, where he received his Ph.D. in 1977 under the supervision of Phillip Griffiths and John T. Tate (''Orbital Integrals on _3''). In 1976 he was assistant professor and later professor at the University of Washington and went in 1989 as a professor to the University of Chicago. He was several times at the Institute for Advanced Study in Princeton, New Jersey (for example, in 1976 and 1977). Kottwitz works in the Langlands program, including harmonic analysis on ''p''-adic Lie groups and automorphic forms and the general linear groups and Shimura varieties. He is a fellow of the American Academy of Arts and Sciences and the American Mathematical Society (AMS). He was an invited speaker at the International Congress of Mathematicians in Berlin in 1998 (Harmonic analysis on semisimple Lie ''p''-adic algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adele Ring
Adele Laurie Blue Adkins (, ; born 5 May 1988), professionally known by the mononym Adele, is an English singer and songwriter. After graduating in arts from the BRIT School in 2006, Adele signed a record deal with XL Recordings. Her debut album, '' 19'', was released in 2008 and spawned the UK top-five singles "Chasing Pavements" and "Make You Feel My Love". The album was certified 8× platinum in the UK and triple platinum in the US. Adele was honoured with the Brit Award for Rising Star as well as the Grammy Award for Best New Artist. Adele released her second studio album, '' 21'', in 2011. It became the world's best-selling album of the 21st century, with sales of over 31 million copies. It was certified 18× platinum in the UK (the highest by a solo artist of all time) and Diamond in the US. According to ''Billboard'', ''21'' is the top-performing album in the US chart history, topping the ''Billboard'' 200 for 24 weeks (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Mathematical Bulletin
The ''Canadian Mathematical Bulletin'' (french: Bulletin Canadien de Mathématiques) is a mathematics journal, established in 1958 and published quarterly by the Canadian Mathematical Society. The current editors-in-chief of the journal are Antonio Lei and Javad Mashreghi. The journal publishes short articles in all areas of mathematics that are of sufficient interest to the general mathematical public. Abstracting and indexing The journal is abstracted in: for the Canadian Mathematical Bulletin. * '''' * '' [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
